Problem: Simplify the following expression: $q = \dfrac{-2y^2 - 24y - 54}{y + 3} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-2$ , so we can rewrite the expression: $ q =\dfrac{-2(y^2 + 12y + 27)}{y + 3} $ Then we factor the remaining polynomial: $y^2 + {12}y + {27} $ ${3} + {9} = {12}$ ${3} \times {9} = {27}$ $ (y + {3}) (y + {9}) $ This gives us a factored expression: $\dfrac{-2(y + {3}) (y + {9})}{y + 3}$ We can divide the numerator and denominator by $(y - 3)$ on condition that $y \neq -3$ Therefore $q = -2(y + 9); y \neq -3$